WILMINGTON, Del. — Books-A-Million Inc.’s directors are being sued by an investor claiming the board wrongfully approved a $48.8 million buyout of the bookstore chain by its controlling shareholders.

Directors of Birmingham, Ala.-based Books-A-Million should be held liable for approving Chairman Clyde Anderson’s offer to pay $3.05 a share in cash to take the chain private, investor Jeffrey Ye said in a Delaware Chancery Court lawsuit. Anderson and his family already own about 53 percent of the company.

“The Anderson family is attempting to buy out the public stockholders at an unfair price, dramatically below the underlying real value of the company, in a transaction that is unfair,” Ye said in the suit, filed Tuesday in Wilmington.

Ann Arbor, Mich.-based Borders, once the U.S.’s second- largest bookseller, is liquidating itself in bankruptcy court after failing to find a buyer for the chain. Borders lost business as customers switched to e-readers such as Amazon.com Inc.’s Kindle, introduced in 2007. Barnes & Noble is the U.S.’s largest bookseller with 1,341 stores.

Jane Hoerner, a Books-A-Million spokeswoman, didn’t immediately return a call for comment on the suit.

Books-A-Million officials said in a release earlier this week that directors had set up a special two-member committee to evaluate the offer by Anderson and his family.

That committee includes J. Barry Mason, the former dean of the University of Alabama’s business school and Albert C. Johnson, a retired accountant and the former head of finance at Dunn Investment Co. Both are current board members.

Ye, the Books-A-Million shareholder who sued in state court in Delaware, said Anderson and his family dominate the company’s board and therefore will control the special committee reviewing the controlling shareholders’ buyout bid.

“The independence of any purported Special Committee must be viewed with a great deal of skepticism,” Ye said in the suit.

Ye filed a so-called derivative suit, which would return any recovery from insurance covering Books-A-Million officers and directors to the company’s coffers.

Books-A-Million, which also runs stores under the names Books & Co., Bookland and Joe Muggs Newsstands, operates in the southeastern United States.